# Electrodynamics I (2021)

Classical electrodynamics is one of the crown jewels of human achievement. What Newton's laws did for the understanding of motion, Maxwell's equations did for a far more mysterious set of phenomena - it unified apparently disconnected phenomena related to electricity, magnetism, and light, and contributed to the discovery of special relativity. Electrodynamics is the simplest gauge field theory - a mathematical structure with beautiful and useful features that is now used to understand essentially all physical phenomena. An area that remains relevant to research owing to its myriad applications, it serves as a starting point for more fancy theory.

## Target Audience

This is the core course ED-1 or P-106 in the TIFR graduate school. If you already had a good course in electrodynamics before coming to TIFR, you should try to drop this course and directly take ED-2.

This page (and Moodle) will be updated regularly with course-related information. Please check frequently.

I am available over email (PLEASE include the tag "ED2021" in the subject line to ensure my spam filter doesn't reject it). You can send anonymous emails if you like. Comments, criticism, cat-gifs, all are welcome.

## Administrivia

**Time:** 2-3 pm, Mondays, Wednesdays and Fridays

**Venue:** Online via zoom

**First lecture:** 17 Feb 2021

**Instructor:** Basudeb Dasgupta (A320)

**Tutor:** Krishnendu Maji

## Course Contents

1. Preliminaries and Maxwell's equations (7 lectures)

2. Electrostatics in vacuum and materials (14 lectures)

3. Magnetostatics in vacuum and materials (6 lectures)

4. Time-varying E and B fields, and their properties (4 lectures)

5. Waves (8 lectures)

Suggested term paper topics: Fundamentals of ED, Optics, Acceleration, Trapping, Radiative Transfer, Waveguides, Membranes, Super/Sub-luminal Light, etc.

## References

1. Modern Electrodynamics, Zangwill (Main Text; *Beware of typos!*)

2. Landau and Lifshitz Vol.2, Landau and Lifshitz

3. Landau and Lifshitz Vol.8, Landau, Lifshitz, and Pitaevskii

4. Classical Electrodynamics, Jackson

5. Feynman Lectures Vol.2, Feynman, Leighton, Sands

## Problem Sets

PS1: Mathematical Background and Maxwell Equations

PS2: Electrostatics

PS3: Magnetostatics

PS4: Time varying E and B fields and Waves

All due by 7 June

## Exams

Midterm: cancelled

Term Paper Presentation: June

Endterm: 29-30 May ; reports due by 13 June

## Lecture Summaries

Day Zero (17 Feb): Course Overview

Introductions

Course contents and expectations (open & honest, aiming to understand just the basics - so that we can apply it to our real lives and research)

Drop test

Lecture 1 (19 Feb): Preliminaries I

Invitation to Electrodynamics

Vectors, Tensors

Curvilinear coordinates

Lecture 2 (22 Feb): Preliminaries II

Derivatives, Integrals, and relevant identities and theorems

Singularities

Lecture 3 (24 Feb): Preliminaries III

Linearity and Fourier techniques

Helmholtz Theorem

Lecture 4 (26 Feb): Maxwell's Equations I

History, Charge, Current, Continuity

Lecture 5 (3 Mar): Maxwell's Equations II

Units, Maxwell's Eqns, Particles vs Fields

Lecture 6 (8 Mar): Maxwell's Equations III

Limits of this theory: Classical vs. Relativistic vs. Quantum, Monopole, Mass of photon, Axions?

Macros vs Micro: Lorentz averaging

Lecture 7 (10 Mar): Maxwell's Equations IV

Derive Maxwell's Equations?

Revision

Lecture 8 (12 Mar): Electrostatics I

Electrodynamics has 4 equations and 4 unknowns

Electrostatic potential via Helmholtz thm

Force, Torque, Work

Earnshaw's thm

Lecture 9 (15 March): Electrostatics II

Surface charge

Matching conditions

Force density

Total energy, Self energy, Potential energy, Interaction energy

Lecture 10 (17 March): Electrostatics III

Multipole expansion of 1/|r-r'|

Identifying the primitive monopole, dipole, quadrupole, multipole of the charge distribution involving source coords

How they couple to the observer coordinate and contribute to potential and work

Lecture 11 (19 March): Electrostatics IV

Dipole, Point dipole

Quadrupole

Traceless multipoles

Lecture 12 (22 March): Electrostatics V

Spherical multipoles

Exterior and Interior expansions

Lecture 13 (24 March): Electrostatics VI

Conductors

Lecture 14 (26 March): Electrostatics VII

Dielectrics

**Droptest (28 March; 1-5pm)**

Lecture 15 (31 March): Electrostatics VIII

Dielectrics

Setting up electrostatic BVPs

Lecture 16 (5 April): Electrostatics IX

BVPs

Uniqueness

Boundary Conditions

Lecture 17 (7 April): Electrostatics X

Grounded conductors

Method of Images

Lecture 18 (9 April): Electrostatics XI

Numerical Solutions

Lecture 19 (12 April): Electrostatics XII

Green's function

Lecture 20 (16 April): Electrostatics XIII

Green's function

Lecture 21 (17 April): Electrostatics XIV

Steady Currents

Ohmic materials

Battery and E fields

Lecture 22 (19 April): Magnetostatics I

Helmholtz+Maxwell = Biot-Savart

Summation problems = Biot-Savart

Setting Up BVP using Scalar Potential and Matching Conditions

Circular Ring

Lecture 23 (21 April): Magnetostatics II

Helmholtz coil, Vector potential BVP in Coulomb gauge

Multipole expansion and vanishing monopole

Lecture 24 (23 April): Magnetostatics III

Multipole moments

Dipole, Magnetic moment, g-2

B fields do no work on moving charges

Lecture 25 (26 April): Magnetostatics IV

Force, Work, Energy

What do B fields look like?

Lecture 26 (28 April): Magnetostatics V

Magnetic materials

Lecture 27 (30 April): Magnetostatics VI

Magnetic Materials

Lecture 28 (3 May): General EM fields I

Displacement/Polarization current and magnetization

Lecture 29 (5 May): General EM field II

Quasi-electrostatics and Quasi-magnetostatics

Charge relaxation and Skin depth

Lecture 30 (7 May): General EM fields III

Poynting vector, linear and angular momentum

Lecture 31 (8 May): General EM fields IV

Energy-momentum conservation

Covariant formulation

Lecture 32 (10 May): Waves I

What are EM waves

Lecture 33 (12 May): Waves II

Solving the vector wave equation

Transverse waves and wavepackets

Lecture 34 (15 May): Waves III

Gaussian beams

Spherical waves

Lecture 35 (19 May): Waves IV

Ponderomotive force

Waves in simple media

Lecture 36 (21 May): Waves V

Waves in simple media

Lecture 37 (22 May): Waves VI

Dispersion

Lecture 38 (24 May): Waves VII

TEM modes in coaxial cable

Basic equations for TE, TM modes

Lecture 39 (26 May): Waves VIII

Waveguides and Cavities

Lecture 40 (28 May): Summary

**Endterm (29, 30 May)**

**Termpapers due on 13 June**

**End of Course (14June): Congratulations!**